This three-week program will explore the emerging field of metric algebraic geometry, where algebraic geometry meets metric and integral geometry. The focus will be on algebraic structures underlying distance functions, curvature and volume formulas, integral geometry, as well as their connections to convex geometry, tame geometry, and optimization.

The scientific program will be structured in three parts: a workshop on the algebraic geometry of Finsler distances; a graduate school offering minicourses on integral geometry, tame geometry and integration, and probabilistic intersection theory; and a concluding conference bringing together leading experts from different areas. The aim is to foster exchange across communities, create a common language, and open new research directions in this rapidly developing field.